Generally, for power transformers, no. Usually if it is important for a transformer to be connected with regard to polarity, there will be a little dot on the schematic, indicating the beginning of the winding. Certain audio and pulse transformers must be wired correctly, but the filament or rectifier couldn't care less of the power phasing.
Lewis L.
This has the same questions as the unnamed post with Ian as the poster
reply to either
Ian:
That depends. If the tubes have cathodes, then the center tap is prabably grounded for hum reduction. Without cathodes, the center tap is probably used to connect the filament to power supply negative, or perhaps to negative through a resistor for grid bias. A winding for two tubes and a pilot light suggests a push-pull output stage, with the center tap being used to bias the filament above negative ground, in order to have a negative bias on the grid with respect to cathode. I would need a schematic of your radio to tell you more.
Lewis L.
Thomas